A family of \(C^1\) - \(P_k\) ( \(k\ge 4\) ) interpolated Galerkin finite elements for the biharmonic equation is constructed on triangular meshes. In this interpolated Galerkin finite element, the interior degrees of freedom are determined by direct interpolation of the right hand side function, and only the rest unknowns are determined by solving the remaining linear equations of the Galerkin projection. In comparison with the traditional finite element method, the interpolated finite element method reduces the number of unknowns from \(O(k^2)\) to O(k) per triangle. Additionally, the method reduces the condition number mostly as if it puts a Dirichlet boundary condition inside every element. The existence and uniqueness of the solution and the optimal order of convergence are proved. The theory is confirmed by numerical tests with \(P_4\) to \(P_8\) finite elements on two meshes.
